Graphs associated with nilpotent Lie algebras of maximal rank.

Díaz, Eduardo, et al. "Graphs associated with nilpotent Lie algebras of maximal rank.." Revista Matemática Iberoamericana 19.2 (2003): 325-338. <http://eudml.org/doc/39704>.

@article{Díaz2003,
abstract = {In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph of this digraph with every isomorphism class of nilpotent Lie algebras of maximal rank and of type A. Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.},
author = {Díaz, Eduardo, Fernández-Mateos, Rafael, Fernández-Ternero, Desamparados, Núñez, Juan},
journal = {Revista Matemática Iberoamericana},
keywords = {Teoría de grafos; Algebra de Lie; Algebra nilpotente; Singularidades; Geometría algebraica; nilpotent Lie algebra; maximal rank; directed graph},
language = {eng},
number = {2},
pages = {325-338},
title = {Graphs associated with nilpotent Lie algebras of maximal rank.},
url = {http://eudml.org/doc/39704},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Díaz, Eduardo
AU - Fernández-Mateos, Rafael
AU - Fernández-Ternero, Desamparados
AU - Núñez, Juan
TI - Graphs associated with nilpotent Lie algebras of maximal rank.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 2
SP - 325
EP - 338
AB - In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph of this digraph with every isomorphism class of nilpotent Lie algebras of maximal rank and of type A. Finally, we show an algorithm which obtains these subgraphs and also groups them in isomorphism classes.
LA - eng
KW - Teoría de grafos; Algebra de Lie; Algebra nilpotente; Singularidades; Geometría algebraica; nilpotent Lie algebra; maximal rank; directed graph
UR - http://eudml.org/doc/39704
ER -